1. Field of the Invention
The present invention relates to a magnetic apparatus such as, for example, a microwave filter, including a magnetic device, e.g., a ferromagnetic resonator, which is formed of yttrium iron garnet (YIG) and which is operated in a d.c. bias magnetic field.
2. Prior Art
A ferromagnetic resonator, e.g., a device using ferrimagnetic resonance of an YIG thin film device, has a resonant frequency which is dependent on the saturation magnetization of the device, and therefore the resonant frequency is directly affected by the temperature characteristics of the saturation magnetization. In order for the YIG thin film device to have a constant resonant frequency (fo) independently of the temperature (T), the device needs to be placed in a thermostatic chamber so that the device is kept at a constant temperature, or biased by an offset magnetic field which is proportional to the temperature dependent variation of the YIG saturation magnetization 4.pi.M.sub.s (Gauss), in addition to the application of a constant d.c. magnetic field which determines the resonant frequency, fo.
Assume in a magnetic circuit, the magnetic field strength Hg in a magnetic gap where a YIG device is placed is given as follows. EQU H.sub.g (T)=(fo/.gamma.)+N.sub.zy .multidot.4.pi.M.sub.sy (T) (1)
where Nzy is the demagnetization factor of YIG, and .gamma. is the gyromagnetic ratio. Accordingly, by varying Hg(T) in proportion to the YIG saturation magnetization 4.pi.M.sub.sy (T) which varies with the temperature T, the resonant frequency, fo, can be maintained constant. Two conceivable methods for varying the magnetic field which are applied to the YIG device in response to the change in the temperature of the device are the use of an electromagnet, and the use of a combination of a permanent magnet and a soft magnetic plate.
However, either the case of using an electromagnet and the case of using a thermostatic chamber requires a supply of energy such as a controlled current from the outside, which results in a complex structure. According to one method of controlling the temperature characteristics of the gap magnetic field H.sub.g with a soft magnetic plate, the gap magnetic field H.sub.g is designed to have the temperature characteristic which is proportional to the temperature characteristic of a ferromagnetic resonator device, e.g., an YIG device, by superimposition of the temperature characteristic of the permanent magnet and the temperature characteristic of the soft magnetic plate so as to compensate for the temperature dependency of the resonant frequency, fo, of the device, whereby fo can be made constant over a wide temperature range.
Illustrated in FIG. 1 is a magnetic circuit consisting of a "C"-shaped yoke 1, which is provided at its confronting end sections with pairs of permanent magnets 2 and soft magnetic plates 3 made of, for example, a ferrite or an alloy of iron, and a magnetic gap 4 with a spacing of l.sub.g which is formed between the soft magnetic plates 3. In the figure, l.sub.m represents the total thickness of the magnet 2, l.sub.x is the total thickness of the soft magnetic plates 3, B.sub.m and H.sub.m are the magnetic flux density and magnetic field strength in each magnet 2, B.sub.x and H.sub.x are the magnetic flux density and magnetic field strength in each soft magnetic plates 3, and B.sub.g and H.sub.g are the magnetic flux density and magnetic field strength in the magnetic gap 4. The permanent magnets 2 are situated in a demagnetizing field, and thus the magnetic field strength H.sub.m is opposite to the magnetic flux density B.sub.m. The CGS unit system is used throughout the following discussion.
The Maxwell's equations for the above-mentioned magnetic circuit are expressed in terms of the magnetic flux density and the magnetic field as follows. ##EQU1##
On the assumption that the magnetic field and magnetic flux density are uniform in the magnet and soft magnetic plates and that there is no magnetic flux leakage outside the circuit, Equations (2) and (3) are reduced as follows to: EQU B.sub.m =B.sub.x =B.sub.g ( 4) EQU l.sub.m .multidot.H.sub.m =l.sub.g .multidot.H.sub.g +l.sub.x .multidot.H.sub.x ( 5)
Provided the magnetization of the soft magnetic plate is 4.pi.M.sub.x, the internal magnetic field H.sub.x of the soft magnetic plate is given as follows. EQU H.sub.x =H.sub.g -N.sub.zx .multidot.4.pi.M.sub.x ( 6)
where N.sub.zx represents the demagnetization factor for the soft magnetic plate, and it is approximated by the following equation when the soft magnetic plate is a thin disk with a diameter of D and a thickness of S(S=1/2l.sub.x). ##EQU2## In case the internal magnetic field of the soft magnetic plate is sufficiently strong, the term 4.pi.M.sub.x in Equation (6) is replaced with the saturation magnetization 4.pi.M.sub.sx.
Substituting Equation (6) into (5), the gap magnetic field Hg is expressed as follows. ##EQU3##
Accordingly, the gap magnetic field Hg is expressed as a function of the temperature T in terms of the internal magnetic field strength H.sub.m (T) and the magnetization strength 4.pi.M.sub.sx (T) of the soft magnetic plate both at a temperature of T, as follows. ##EQU4##
Accordingly, by choosing the characteristics and dimensions of the magnets 2 and the soft magnetic plates 3 and the length of the gap, i.e., H.sub.m, 4.pi.M.sub.sx, N.sub.zx, l.sub.m, l.sub.x, and l.sub.g, an optimum H.sub.g can be obtained from Equation (9).
In practice, the characteristics of the soft magnetic plate are adjusted so that, for example, by choosing the composition and sintering condition of ferrite, by choosing the composition of the alloy, or by using several kinds of soft magnetic plates in combination. However, even for the selection of the composition and processing conditions of the soft magnetic plate, it is extremely difficult to model the H.sub.g to the desired temperature characteristics of the ferromagnetic resonator device so as to obtain the proper slope and curvature. For this reason, it has not been feasible to maintain constant the resonant frequency, fo, of a ferrimagnetic resonator device, e.g., YIG device, over a wide temperature range.